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Inverse Random Source Scattering for the Helmholtz Equation with Attenuation
SIAM Journal on Applied Mathematics ( IF 1.9 ) Pub Date : 2021-04-08 , DOI: 10.1137/19m1309456
Peijun Li , Xu Wang

SIAM Journal on Applied Mathematics, Volume 81, Issue 2, Page 485-506, January 2021.
In this paper, a new model is proposed for the inverse random source scattering problem of the Helmholtz equation with attenuation. The source is assumed to be driven by a fractional Gaussian field whose covariance is represented by a classical pseudodifferential operator. The work contains three contributions. First, the connection is established between fractional Gaussian fields and rough sources characterized by their principal symbols. Second, the direct source scattering problem is shown to be well-posed in the distribution sense. Third, we demonstrate that the micro-correlation strength of the random source can be uniquely determined by the passive measurements of the wave field in a set which is disjoint with the support of the strength function. The analysis relies on careful studies on the Green function and Fourier integrals for the Helmholtz equation.


中文翻译:

带有衰减的Helmholtz方程的逆随机源散射

SIAM应用数学杂志,第81卷,第2期,第485-506页,2021年1月。
本文针对带衰减的亥姆霍兹方程的逆随机源散射问题提出了一个新的模型。假定源由分数高斯场驱动,分数高斯场的协方差由经典的伪微分算子表示。这项工作包含三个方面。首先,在分数高斯场和以其主要符号为特征的粗糙源之间建立联系。第二,直接源散射问题在分布意义上被证明是恰当的。第三,我们证明了随机源的微相关强度可以通过对波场的被动测量来唯一确定,而该场在强度函数的支持下是不相交的。
更新日期:2021-04-20
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